Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import math

n = int(raw_input())

k = 1
ok = False
while (k * (k + 1) / 2) < n:
    r = k * (k + 1) / 2
    c = n - r
    c *= -2

    s = int((-1 + math.sqrt(1 - 4 * c)) / 2)
    t = s * (s + 1) / 2

    if t + r == n :
        ok = True
        break

    k += 1

if ok:
    print "YES"
else:
    print "NO"